Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers |
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Authors: | A Uma Maheswari P Prema S Mahadevan and C S Shastry |
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Institution: | (2) Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, Russia;(3) Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, USA; |
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Abstract: | In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the
quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate
their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The
energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are
also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states
with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula
which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar
formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies
as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission,
reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the
same order of magnitude as lifetime of the quasi-bound state, but somewhat larger. |
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